In this digital ITEMS module, Dr. Stella Kim provides an overview of multidimensional item response theory (MIRT) equating. Traditional unidimensional item response theory (IRT) equating methods impose the sometimes untenable restriction on data that only a single ability is assessed. This module discusses potential sources of multidimensionality…

Population invariance is a desirable property of test equating which might not hold when significant changes occur in the test population, such as those brought about by the COVID-19 pandemic. This research aims to investigate whether equating functions are reasonably invariant when the test population is impacted by the pandemic. Based on…

Test equating requires collecting data to link the scores from different forms of a test. Problems arise when equating samples are not equivalent and the test forms to be linked share no common items by which to measure or adjust for the group nonequivalence. Using data from five operational test forms, we created five pairs of research forms for…

Commonly used machine learning applications seem to relate to big data. This article provides a gentle review of machine learning and shows why machine learning can be applied to small data too. An example of applying machine learning to screen irregularity reports is presented. In the example, the support vector machine and multinomial naïve…

The choice of anchor tests is crucial in applications of the nonequivalent groups with anchor test design of equating. Sinharay and Holland (2006, 2007) suggested "miditests," which are anchor tests that are content-representative and have the same mean item difficulty as the total test but have a smaller spread of item difficulties.…

Calibration and equating is the quintessential necessity for most large-scale educational assessments. However, there are instances when no consideration is given to the equating process in terms of context and substantive realization, and the methods used in its execution. In the view of the authors, equating is not merely an exhibit of the…

A goal for any linking or equating of two or more tests is that the linking function be invariant to the population used in conducting the linking or equating. Violations of population invariance in linking and equating jeopardize the fairness and validity of test scores, and pose particular problems for test-based accountability programs that…

This module describes and extends X-to-Y regression measures that have been proposed for use in the assessment of X-to-Y scaling and equating results. Measures are developed that are similar to those based on prediction error in regression analyses but that are directly suited to interests in scaling and equating evaluations. The regression and…

We make a distinction between two types of test changes: inevitable deviations from specifications versus planned modifications of specifications. We describe how score equity assessment (SEA) can be used as a tool to assess a critical aspect of construct continuity, the equivalence of scores, whenever planned changes are introduced to testing…

The study examined two approaches for equating subscores. They are (1) equating subscores using internal common items as the anchor to conduct the equating, and (2) equating subscores using equated and scaled total scores as the anchor to conduct the equating. Since equated total scores are comparable across the new and old forms, they can be used…

This article presents the author's observations on Neil Dorans's NCME Career Award Address: "The Contestant Perspective on Taking Tests: Emanations from the Statue within." He calls attention to some points that Dr. Dorans made in his address, and offers his thoughts in response.

Views on testing--its purpose and uses and how its data are analyzed--are related to one's perspective on test takers. Test takers can be viewed as learners, examinees, or contestants. I briefly discuss the perspective of test takers as learners. I maintain that much of psychometrics views test takers as examinees. I discuss test takers as a…

Over the past few decades, those who take tests in the United States have exhibited increasing diversity with respect to native language. Standard psychometric procedures for ensuring item and test fairness that have existed for some time were developed when test-taking groups were predominantly native English speakers. A better understanding of…

This article discusses a particular type of concordance table and the potential for test score misuse that may result from employing such a table. The concordance that is discussed is typically created between scores on different, nonequatable versions of a test that share the same or close to the same test title. These concordance tables often…

In large-scale assessments, such as state-wide testing programs, national sample-based assessments, and international comparative studies, there are many steps involved in the measurement and reporting of student achievement. There are always sources of inaccuracies in each of the steps. It is of interest to identify the source and magnitude of…